Communication: equation of state of hard oblate ellipsoids by replica exchange Monte Carlo

We implemented the replica exchange Monte Carlo technique to produce the equation of state of hard 1:5 aspect-ratio oblate ellipsoids for a wide density range. For this purpose, we considered the analytical approximation of the overlap distance given by Bern and Pechukas and the exact numerical solution given by Perram and Wertheim. For both cases we capture the expected isotropic-nematic transition at low densities and a nematic-crystal transition at larger densities. For the exact case, these transitions occur at the volume fraction 0.341, and in the interval 0.584-0.605, respectively.     

Crystal nucleation in binary hard sphere mixtures: a Monte Carlo simulation study

We present calculations of the nucleation barrier during crystallization in binary hard sphere mixtures under moderate degrees of supercooling using Monte Carlo simulations in the isothermal-isobaric semigrand ensemble in conjunction with an umbrella sampling technique. We study both additive and negatively nonadditive binary hard sphere systems. The solid-fluid phase diagrams of such systems show a rich variety of behavior, ranging from simple spindle shapes to the appearance of azeotropes and eutectics to the appearance of substitutionally ordered solid phase compounds. We investigate the effect of these types of phase behavior upon the nucleation barrier and the structure of the critical nucleus. We find that the underlying phase diagram has a significant effect on the mechanism of crystal nucleation. Our calculations indicate that fractionation of the species upon crystallization increases the difficulty of crystallization of fluid mixtures and in the absence of fractionation (azeotropic conditions) the nucleation barrier is comparable to pure fluids. We also calculate the barrier to nucleation of a substitutionally ordered compound solid. In such systems, which also show solid-solid phase separation, we find that the phase that nucleates is the one whose equilibrium composition is closer to the composition of the fluid phase.     

Critical flux of hard sphere suspensions in crossflow filtration: Hydrodynamic force bias Monte Carlo simulations

A Monte Carlo method is developed for crossflow membrane filtration to determine the critical flux of hard sphere suspensions. Brownian and shear-induced diffusion are incorporated into an effective hydrodynamic force exerted on the hard spheres in a concentrated shear flow. Effects of shear rate and particle size on the critical flux are investigated using hydrodynamic force bias Monte Carlo simulations, providing a baseline of the critical flux.     

Monte Carlo simulations of two-dimensional hard core lattice gases

Monte Carlo simulations are used to study lattice gases of particles with extended hard cores on a two-dimensional square lattice. Exclusions of one and up to five nearest neighbors (NN) are considered. These can be mapped onto hard squares of varying side length, lambda (in lattice units), tilted by some angle with respect to the original lattice. In agreement with earlier studies, the 1NN exclusion undergoes a continuous order-disorder transition in the Ising universality class. Surprisingly, we find that the lattice gas with exclusions of up to second nearest neighbors (2NN) also undergoes a continuous phase transition in the Ising universality class, while the Landau-Lifshitz theory predicts that this transition should be in the universality class of the XY model with cubic anisotropy. The lattice gas of 3NN exclusions is found to undergo a discontinuous order-disorder transition, in agreement with the earlier transfer matrix calculations and the Landau-Lifshitz theory. On the other hand, the gas of 4NN exclusions once again exhibits a continuous phase transition in the Ising universality class-contradicting the predictions of the Landau-Lifshitz theory. Finally, the lattice gas of 5NN exclusions is found to undergo a discontinuous phase transition.     

Equilibrium states of self-assembly systems: Monte Carlo simulations

We investigated the equilibrium states of the self-assembly of amphiphilic molecules in water. The amphiphiles are represented by chains of the type H1T4, where H is the hydrophilic part of the molecule and T is its hydrophobic portion formed by four monomers. We have performed Monte Carlo simulations on a two-dimensional lattice, in which each water molecule occupies a single site, and the amphiphiles occupy five sites of the lattice. We have determined the aggregate distribution curves for the system at low concentration and fixed temperature. We have shown that the criterion to determine the equilibrium states of the system, based on the stabilization of energy curves as a function of the simulation time, is not reliable. The best way to ensure that the equilibrium state was reached was to follow the route to equilibrium of all aggregate sizes of the system.     

Elastic properties of soft sphere crystal from Monte Carlo simulations

Elastic properties of faced centered cubic (fcc) crystals composed of soft spheres, interacting through potentials of the form u(r) ~ r(-n), have been investigated by Monte Carlo (MC) simulations. It is shown that both the softness parameter (n(-1)) and temperature strongly influence the elastic properties of the studied system. The simulations show explicitly that when T > 0 the elastic constants of the hard sphere crystal can be obtained by taking the limit n --> infinity of soft spheres. When T --> 0 for any finite n, the elastic constants of the soft spheres tend to those of the static model. At all temperatures and softness parameters studied here, n, the Poisson's ratio in [110] (perpendicular direction) is negative.     

Monte Carlo study of four dimensional binary hard hypersphere mixtures

A multithreaded Monte Carlo code was used to study the properties of binary mixtures of hard hyperspheres in four dimensions. The ratios of the diameters of the hyperspheres examined were 0.4, 0.5, 0.6, and 0.8. Many total densities of the binary mixtures were investigated. The pair correlation functions and the equations of state were determined and compared with other simulation results and theoretical predictions. At lower diameter ratios the pair correlation functions of the mixture agree with the pair correlation function of a one component fluid at an appropriately scaled density. The theoretical results for the equation of state compare well to the Monte Carlo calculations for all but the highest densities studied.     

Mode excitation Monte Carlo simulations of mesoscopically large membranes

Solvent-free coarse grained models represent one of the most promising approaches for molecular simulations of mesoscopically large membranes. In these models, the size of the simulated membrane is limited by the slow relaxation time of the longest bending mode. Here, we present a Monte Carlo algorithm with update moves in which all the lipids are simultaneously displaced. These collective moves result in fast excitation and relaxation of the long wavelength thermal fluctuations. We apply the method to simulations of a bilayer membrane with linear size of approximately 50 nm and show reduction in the relaxation time by two orders of magnitudes when compared to conventional Monte Carlo.     

N]pT Monte Carlo simulations of the cluster-crystal-forming penetrable sphere model

Certain models with purely repulsive pair interactions can form cluster crystals with multiply-occupied lattice sites. Simulating these models' equilibrium properties is, however, quite challenging. Here, we develop an expanded isothermal-isobaric [N]pT ensemble that surmounts this problem by allowing both particle number and lattice spacing to fluctuate. It is particularly efficient at high T, where particle insertion is facile. Using this expanded ensemble and thermodynamic integration, we solve the phase diagram of a prototypical cluster-crystal former, the penetrable sphere model, and compare the results with earlier theoretical predictions. At high temperatures and densities, the equilibrium occupancy n(c)(eq) of face-centered cubic crystal increases linearly. At low temperatures, although n(c)(eq) plateaus at integer values, the crystal behavior changes continuously with density. The previously ambiguous crossover around T ~ 0.1 is resolved.     

Titration of hydrophobic polyelectrolytes using Monte Carlo simulations

The conformation and titration curves of weak (or annealed) hydrophobic polyelectrolytes have been examined using Monte Carlo simulations with screened Coulomb potentials in the grand canonical ensemble. The influence of the ionic concentration pH and presence of hydrophobic interactions has been systematically investigated. A large number of conformations such as extended, pearl-necklace, cigar-shape, and collapsed structures resulting from the subtle balance of short-range hydrophobic attractive interactions and long-range electrostatic repulsive interactions between the monomers have been observed. Titration curves were calculated by adjusting the pH-pK(0) values (pK(0) represents the intrinsic dissociation constant of an isolated monomer) and then calculating the ionization degree alpha of the polyelectrolyte. Important transitions related to cascades of conformational changes were observed in the titration curves, mainly at low ionic concentration and with the presence of strong hydrophobic interactions. We demonstrated that the presence of hydrophobic interactions plays an important role in the acid-base properties of a polyelectrolyte in promoting the formation of compact conformations and hence decreasing the polyelectrolyte degree of ionization for a given pH-pK(0) value.     

Monte Carlo simulations of a liquid crystal copolymer in the solid state

The condensed phase of the alternating copolyester of p-hydroxybenzoic acid (HBA) and 2-hydroxy-6-naphthoic acid (HNA) is investigated by studying the room temperature packing arrangement of the copolymer chains. A molecular modeling methodology is employed with a Monte Carlo sampling of the configurational phase space. Realistic poly(HBA-alt-HNA) polymer chains are represented by an explicit atom representation of the HBA/HNA dimers. States are sampled from the NVT ensemble using a sampling scheme consisting of (1) valence and torsional variations, (2) rigid body rotations of the chain about the chain axis, and (3) rigid body translations of the chain. The effect of chain packing on the conformation of chains, as well as the relative intra- and intermolecular orientations of aromatic rings, is investigated. Correlation of chain positioning along the chain axis is dominated by aromatic rings maintaining a center-to-center plane of registry. These layers of aromatic units pack with a preference for edge-to-face orientations in a herringbone-type pattern and have an intermolecular ring angle between the pairs of aromatic rings in the unit cell that is ca. 68°. The aromatic rings, on average, are rotated 38° out from the b–c plane. The phenylene rings of these copolyesters are less restricted in their relative orientation in comparison to the naphthalene rings. Intramolecular orientational probability density distributions indicate a preference for staggering the successive aromatic rings along the chain, with a staggering angle of ca. 66°. © 1998 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 36: 727–741, 1998     

Communication: inferring the equation of state of a metastable hard-sphere fluid from the equation of state of a hard-sphere mixture at high densities

A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency.     

Poisson's ratio of the fcc hard sphere crystal at high densities

Elastic constants and the Poisson ratio of the fcc hard-sphere crystalline phases, free of defects and with vacancies, are determined by two Monte Carlo methods: (i) the analysis of the box fluctuations in the constant pressure ensemble with variable box shape (N-P-T) and (ii) by the free-energy differentiation with respect to deformation in the fixed box ensemble (N-V-T). Very good agreement is observed for the extrapolated to the infinitely large system limit results of both the methods. The coefficients of the leading singularities of the elastic constants near close packing are estimated; they are well described by the free volume approximation. Two mechanisms influencing the Poisson ratio are studied. (i) It is shown that at high densities particle motions decrease the Poisson ratio with respect to the static case which corresponds to zero temperature. Simulations performed for systems of soft spheres, interacting through n-inverse-power potentials, r-n, show that the elastic constants of the hard spheres can be obtained in the limit n-->infinity. When T-->0 the elastic constants of the soft spheres tend to those of the static model. (ii) It is also shown that vacancies decrease C11 and C44 and increase C12 and, hence, increase the Poisson ratio with respect to the defect-free state of the system.     

Optimization of 89Zr production using Monte Carlo simulations

Zirconium-89 (⁸⁹Zr) can be produced in a cyclotron by focusing the proton beam on an yttrium-89 (⁸⁹Y) foil target. Optimal combination of beam energy and target assembly configuration enables maximum production of ⁸⁹Zr while minimizing the formation of contaminant nuclides such as ⁸⁸Zr and ⁸⁸Y to allow efficient and effective radiopharmaceutical labeling. Accurate modeling of the proton beam and the target is therefore an essential step to assure the best beam and target specification. We used the radiation transport code MCNPX to simulate the transport of protons through the irradiation assembly and the nuclear reaction code TALYS to obtain the production cross sections of various nuclides from proton-⁸⁹Y reactions. Results from simulating the irradiation of 14 mm diameter targets with aluminum (Al) degrader at 19.8 mA for 1 h suggested that the 0.15 mm thick one would produce 227 MBq while the 0.3 mm thick one would produce 413 MBq of ⁸⁹Zr with less than 1 % uncertainty. These results show excellent agreement with experimental work in literature. This work provides the basis for further experimental and theoretical assessments of the use of ⁸⁹Zr as radiopharmaceutical labels.     

Monte Carlo simulations of the exchange kinetics of polymers adsorbed on a solid surface

The exchange kinetics of polymers adsorbing on a solid surface is extensively studied by dynamic Monte Carlo simulations. A model employed simulates a semidilute polymer solution placed in contact with a solid surface that attracts polymer segments by the adsorption interaction (χ_s). The exchange process of polymer chains, between the solution and the adsorbed polymer layer, is examined under various conditions. The exchange kinetics shows two characteristic regimes with increasing chain length. One is the diffusion‐controlled regime found with a small χ_s , and the other the detachment‐controlled regime with a large χ_s . These two regimes are well described by a kinetic theory. Various dynamic quantities show that the diffusion‐controlled regime is not due to sluggish dynamics near the surface, but rather to bulk diffusion of chains. The diffusion‐controlled regime found in this study is considered to appear at the high temperature limit.     

Adsorption of a binary mixture of adhesive fluids in planar pores: a Monte Carlo study

Grand canonical Monte Carlo simulation is used to study the adsorption of a binary sticky hard-sphere fluid mixture in planar pores. The wall-component 1 and wall-component 2 contact densities are determined to calculate the pressure as a function of the composition of the mixture and the separation between the walls. From these data dependence of the solvation force between the plates on pore width is estimated. The simulation results are compared with the predictions of the Percus-Yevick approximation for planar pores. The density profiles of particular components show interesting shapes stemming from the interplay between the steric effects and the competitive adhesion among all possible species pairs. It is shown that narrowing of the pore causes selective partitioning of individual components of the mixture between the bulk phase and the interior of the pore. The agreement between the two methods is better at wider pores and for the component comprised of weakly adhesive particles.     

Thermodynamic derivative properties and densities for hyperbaric gas condensates: SRK equation of state predictions versus Monte Carlo data

The ability of Soave–Redlich–Kwong cubic equation of state (SRK EoS) to predict densities and thermodynamic derivative properties such as thermal expansivity, isothermal compressibility, calorific capacity, and Joule–Thompson coefficients, for two gas condensates over a wide range of pressures (up to 110 MPa) was studied. The predictions of the EoS were compared to Monte Carlo simulation data obtained by Lagache et al. [M.H. Lagache, P. Ungerer, A. Boutin, Fluid Phase Equilibr. 220 (2004) 221]. Two completely different alpha functions for the SRK EoS attractive term were used and their respective effects on the predictions of such properties were analyzed. Also, two different forms of the crossed terms of the attractive parameter, a_ij, and three expressions of the crossed terms of the repulsive parameter, b_ij, were combined in different ways, and predictions were carried out. Little sensitivity of the properties on the chosen alpha function, except for the calorific capacities, was found in the systems studied. The most commonly used combination rules to model phase behavior of reservoir fluids, i.e. geometric and arithmetic forms of a_ij and b_ij, respectively, predicted very deficient results for these fluids at extreme conditions, specially for density calculations.     

Determining the efficiency of a broad-energy HPGe detector using Monte Carlo simulations

Broad-energy HPGe detectors have a useful range of 3 keV to 3 MeV, making them ideal for the assay of environmental samples. Such measurements however, are hindered by variations in the sample matrix, summing effects, and the Compton continuum. Detectors may be characterised by proprietary software in such a situation, however Monte-Carlo modelling is a useful, inexpensive alternative that also provides greater flexibility when determining the detector response and efficiency during a measurement. In the current work, a full GEANT4 model of a broad-energy HPGe detector is presented, and simulations of various samples are compared to experimental data. These are found to be accurate within 3 % at a confidence level of 95 % for energies from 30 to 3,000 keV, with greater variations below 100 keV due to an increased sensitivity to geometrical inaccuracies.